Our knowledge of the universe may be arranged in several related categories: Matter, Structure, and Force and Energy.
Matter is the "stuff" that the Universe is made of. We recognize as facts that every bit of matter must always be someplace, and fully occupies that particular place at that time.
Structure describes how various bits of matter may be arranged, by position and velocity, relative to one another, and how those arrangements may change over time.
Forces may maintain certain structures of matter, or cause structures to change over time.
Energy is inherent in any Structure, because Forces between the parts of a structure represent a form of potential energy.
Some Changes in structure may either go to a state of higher potential energy, and thus require additional energy, or go to a state of lower potential energy, and thus produce excess energy.
Structural changes that produce excess energy may in some cases dispose of it by emitting waves, while changes that require additional energy may in some cases get it by absorbing waves.
Mechanical Waves
As the name suggests, mechanical waves must travel through something, a solid, liquid or gas. Although there are several modes of wave motion, they all share the fact that the motion is transferred from one region to the next, essentially by particles bumping into each other, in any medium, and in solids only, also by tugging on each other.
The interactions cover small distances, but happen very frequently and in large numbers, allowing the wave to travel quickly. A common misunderstanding is that the wave transfers material from place to place, but little or no transfer takes place.
We have covered these lessons:
We learned that seemingly different mechanical systems have similar behavior, but some differences.
We observed that any such system has a stable position, where it has minimum energy.
If energy is applied to move the system away from the stable position, the restoring force will act to return it to that position.
But when the stable position is reached, the system will be in motion, and momentum will carry it beyond the stable position.
From there, the restoring will again act, and the cycle will repeat
What was the same? Repeating motion at a steady frequency, with gradual return to the stable position.
What was different?
Mass on Spring frequency depended on both mass and spring stiffness.
Pendulum frequency did not depend on mass, only length of support. Why?
What was surprising? Two surprises:
Frequency remained constant as amplitude decreased.
Remark, just by similarity to Simple Harmonic Motion, we might expect a stronger restoring force to give faster wave speed, and a heavier mass density to give a slower speed. That turns out to be true.
And we might expect yhe Amplitude to have no effect on speed. That turns out to be true as well.
We know that every system of SHM has a natural frequency, but can be forced to move at any other frequency.
So we might ask, again, just by similarity to Simple Harmonic Motion, if a fluid has a "best" frequency, at which the speed is higher? But that turns out to be false.
We have learned that a simple sound is a sine wave. But most things produce sounds that are a combination of sine waves.
They are usally harmonics, which are at multiples of the basic frequency, and some are stronger than others, but all contribute to the sound we hear. Hearing these complex sounds, it is hard to know just how they are made. But we now have tools that help us to visualize them
Mechanical Waves
As the name suggests, mechanical waves must travel through something, a solid, liquid or gas. Although there are several modes of wave motion, they all share the fact that the motion is transferred from one region to the next, essentially by particles bumping into each other, in any medium, and in solids only, also by tugging on each other.
The interactions cover small distances, but happen very frequently and in large numbers, allowing the wave to travel quickly. A common misunderstanding is that the wave transfers material from place to place, but little or no transfer takes place.
We have covered these lessons:
We learned that seemingly different mechanical systems have similar behavior, but some differences.
We observed that any such system has a stable position, where it has minimum energy.
If energy is applied to move the system away from the stable position, the restoring force will act to return it to that position.
But when the stable position is reached, the system will be in motion, and momentum will carry it beyond the stable position.
From there, the restoring will again act, and the cycle will repeat
- Wave Creation and Propagation : Ocean Waves, Transverse and Longitudinal Waves
The fundamental difference between a system in periodic motion and a wave:This lesson shows that there are several types of mechanical wave possible:
- Wavelength, Frequency, Speed of Sound in Air, Water, Solids Resonance and Standing Waves
Remark, just by similarity to Simple Harmonic Motion, we might expect a stronger restoring force to give faster wave speed, and a heavier mass density to give a slower speed. That turns out to be true.And we might expect yhe Amplitude to have no effect on speed. That turns out to be true as well.
We know that every system of SHM has a natural frequency, but can be forced to move at any other frequency.
So we might ask, again, just by similarity to Simple Harmonic Motion, if a fluid has a "best" frequency, at which the speed is higher? But that turns out to be false.
- Waveforms
We have learned that a simple sound is a sine wave. But most things produce sounds that are a combination of sine waves.They are usally harmonics, which are at multiples of the basic frequency, and some are stronger than others, but all contribute to the sound we hear.
Hearing these complex sounds, it is hard to know just how they are made. But we now have tools that help us to visualize them